An Unbiased Estimator of Peculiar Velocity with Gaussian Distributed Errors for Precision Cosmology

We introduce a new estimator of the peculiar velocity of a galaxy or group of galaxies from redshift and distance estimates. This estimator results in peculiar velocity estimates which are statistically unbiased and that have errors that are Gaussian distributed, thus meeting the assumptions of analyses that rely on individual peculiar velocities. We apply this estimator to the SFI++ and the Cosmicflows-2 catalogs of galaxy distances and, using the fact that peculiar velocity estimates of distant galaxies are error dominated, examine their error distributions, The adoption of the new estimator significantly improves the accuracy and validity of studies of the large-scale peculiar velocity field and eliminates potential systematic biases, thus helping to bring peculiar velocity analysis into the era of precision cosmology. In addition, our method of examining the distribution of velocity errors should provide a useful check of the statistics of large peculiar velocity catalogs, particularly those that are compiled out of data from multiple sources.Comment: 6 Pages, 5 Figure

Theoretical Expectations for Bulk Flows in Large Scale Surveys

We calculate the theoretical expectation for the bulk motion of a large scale survey of the type recently carried out by Lauer and Postman. Included are the effects of survey geometry, errors in the distance measurements, clustering properties of the sample, and different assumed power spectra. We consider the power spectrum calculated from the IRAS--QDOT survey, as well as spectra from hot $+$ cold and standard cold dark matter models. We find that sparse sampling and clustering can lead to an unexpectedly large bulk flow, even in a very deep survey. Our results suggest that the expected bulk motion is inconsistent with that reported by Lauer and Postman at the $90-94\%$ confidence level.Comment: 13 pages, uuencoded compressed postscript file with two figures and a table enclosed, UM-AC-93-2

The Cosmic Mach Number: Comparison from Observations, Numerical Simulations and Nonlinear Predictions

We calculate the cosmic Mach number M - the ratio of the bulk flow of the velocity field on scale R to the velocity dispersion within regions of scale R. M is effectively a measure of the ratio of large-scale to small-scale power and can be a useful tool to constrain the cosmological parameter space. Using a compilation of existing peculiar velocity surveys, we calculate M and compare it to that estimated from mock catalogues extracted from the LasDamas (a LCDM cosmology) numerical simulations. We find agreement with expectations for the LasDamas cosmology at ~ 1.5 sigma CL. We also show that our Mach estimates for the mocks are not biased by selection function effects. To achieve this, we extract dense and nearly-isotropic distributions using Gaussian selection functions with the same width as the characteristic depth of the real surveys, and show that the Mach numbers estimated from the mocks are very similar to the values based on Gaussian profiles of the corresponding widths. We discuss the importance of the survey window functions in estimating their effective depths. We investigate the nonlinear matter power spectrum interpolator PkANN as an alternative to numerical simulations, in the study of Mach number.Comment: 12 pages, 9 figures, 3 table

Structure in a Loitering Universe

We study the formation of structure for a universe that undergoes a recent loitering phase. We compare the nonlinear mass distribution to that in a standard, matter dominated cosmology. The statistical aspects of the clustered matter are found to be robust to changes in the expansion law, an exception being that the peculiar velocities are lower by a factor of $\sim 3$ in the loitering model. Further, in the loitering scenario, nonlinear growth of perturbation occurs more recently ($z\sim 3-5$) than in the matter dominated case. Differences in the high redshift appearances of the two models will result but observable consequences depend critically on the chosen form, onset and duration of the loitering phase.Comment: 8 pages, (uses revtex.sty), 5 figures not included, available on request, UM AC 92-

Current Status Of Velocity Field Surveys: A Consistency Check

We present an analysis comparing the bulk--flow measurements for six recent peculiar velocity surveys, namely, ENEAR, SFI, RFGC, SBF and the Mark III singles and group catalogs. We study whether the direction of the bulk--flow estimates are consistent with each other and construct the full three dimensional bulk--flow vectors for each survey. We show that although the surveys differ in their geometry, galaxy morphologies, distance measures and measurement errors, their bulk flow vectors are expected to be highly correlated and in fact show impressive agreement in all cases. We found a combined weighted mean bulk motion of 330 km s$^{-1}$ $\pm 101$ km s$^{-1}$ toward $l= 234^{\degree}\pm 11^{\degree}$ and $b=12^{\degree}\pm 9^{\degree}$ in a sphere with an effective depth of $\sim4000$ km s$^{-1}$.Comment: 16 pages, 2 figures 2 tables, minor changes, reflects published versio

Large Scale Velocity Fields Present and Future: Making Sense of the data

The large scale velocity field was sampled recently by two independent methods: the supernovae type Ia light curve shapes (Riess, Press \& Kirshner) and the Abell Cluster Catalog brightest cluster galaxy metric luminosity (Lauer \& Postman). The results of these investigations seem to be contradictory. I present an analysis of these samples, compare them and investigate whether standard structure formation models and other deep surveys are compatible with them. I also make suggestions as to how to improve the samples so we can actually resolve the bulk flow vectors. I show that although these two samples seem to cover the same volume, their window functions are sufficiently different so that they are only weakly correlated. Further, since both samples are sparse, they are noise dominated and in order to improve the signal to noise they need to either increase their sample size (RPK) or decrease the measurement errors (LP) significantly.Comment: 8 pages, 3 figures included in a self-unpacking uudecoded gzipped tarred postscript file. A lecture presented in the ASP conference on "Clusters, Lensing and the Future of the Universe". College Park, MD, June 26--28, 1995, Ed. V. Trimble (ASP Conference Series). The tarred file is available at http://pupgga.princeton.edu/disk20/anonymous/feldman/ASP.ta

Power Spectrum Analysis of Large Baseline Redshift Surveys ♣

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/73588/1/j.1749-6632.1993.tb43927.x.pd